the main problem with the non-snowflake tires is actually the rubber itself as opposed to the tread pattern. Non-snowflake tires tend to harden up at temperatures as high as 7 degrees C (45 ish F). The harder your tires are the less likely you are to get good road contact. Winter tires are made of much softer rubbers that stay pliable at much lower temperatures.
On my previous truck I ran fairly aggressive all-terrain tires year round. I got a good deal on some studded winter tires this winter and put them on my new Cherokee. I can say that the softer rubber definitely stays more pliable. For my old truck I would get "square" tires at -20C from sitting overnight as the rubber would harden up and flat spots would develop. I've yet to experience that with the winter tires on my Cherokee and generally winter tires stay pliable to about -30C. I drive the same Alaska Hwy as @ArcticLyn
though I have to drive 457km (286 miles) each way for groceries (572 mile round trip) as I'm further out than her! I chose the studs because our snow conditions are generally hard packed snow/ice. It just gives me extra peace of mind. That being said things are most slippery during the 'warmer' cold temperatures and in high traffic areas such as intersections where layers of water build up on the ice/snow making things extra slippy. Once you hit -35 C or so things get slightly more sticky again. I will say my Cherokee is pretty unstoppable in snow mode with these tires/studs. Now, I only slid once on my previous all-terrains on my truck but, it was fairly warm and thus slippery and it was straight through a busy intersection on black ice in Anchorage...not something I enjoyed.. I didn't bother changing the wheels as we don't use as much salt up here as some more southern parts of Canada as salt loses effectiveness below certain temperatures (it's mostly, though not entirely sand up here). Winter rims however do make it much faster to change your tires and makes it easier to do it yourself if you're so inclined. Salt plays havoc on alloy wheels so that may also be a consideration for you.
Studs are legal in all Provinces/Territories in Canada except for Ontario. In Ontario they are allowed in Northern Ontario only (areas defined in regulations). In some Provinces/Territories they are only allowed during certain times of the year (even in the ones with no restrictions I don't know why you'd run studs in summer!). In Alaska they are also allowed seasonally. There is some debate still on whether studs are a necessity these days with new tire tech but, some people love 'em, some don't see the need. It does add about $20 a tire give or take.
The downside is because winter tires are softer they will wear much faster. Generally as a result winter tires don't have an expected mileage life. So don't run winter tires year round or you're going to be replacing your tires very frequently! If you push lots of snow/slush look for tires with good siping, which helps displace the snow/slush.
In some provinces in Canada snowflake rated tires or M+S tires are required during certain times of the year (note M+S tires are not snowflake winter tires but a slightly better all-season tire). In Quebec it is required on all roads. In BC, certain roads are designated as highways where you are required to have snowflake rated or M+S tires in the winter (usually highways in Northern BC/snowbelt areas)